Bivariate Poisson distribution
Probability mass function and random generation for the bivariate Poisson distribution.
dbvpois(x, y = NULL, a, b, c, log = FALSE) rbvpois(n, a, b, c)
x, y |
vectors of quantiles; alternatively x may be a two-column matrix (or data.frame) and y may be omitted. |
a, b, c |
positive valued parameters. |
log |
logical; if TRUE, probabilities p are given as log(p). |
n |
number of observations. If |
Probability mass function
f(x) = exp(-(a+b+c)) * (a^x)/x! * (b^y)/y! * sum(choose(x,k)*choose(y,k)*k!*(c/(a*b))^k)
Karlis, D. and Ntzoufras, I. (2003). Analysis of sports data by using bivariate Poisson models. Journal of the Royal Statistical Society: Series D (The Statistician), 52(3), 381-393.
Kocherlakota, S. and Kocherlakota, K. (1992) Bivariate Discrete Distributions. New York: Dekker.
Johnson, N., Kotz, S. and Balakrishnan, N. (1997). Discrete Multivariate Distributions. New York: Wiley.
Holgate, P. (1964). Estimation for the bivariate Poisson distribution. Biometrika, 51(1-2), 241-287.
Kawamura, K. (1984). Direct calculation of maximum likelihood estimator for the bivariate Poisson distribution. Kodai mathematical journal, 7(2), 211-221.
x <- rbvpois(5000, 7, 8, 5) image(prop.table(table(x[,1], x[,2]))) colMeans(x)
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